Practically, the features discussed above depend strongly on the
parameters of the NGN junctions, such as the device length and/or
the Fermi energy. It results from the fact that the charge transport
can be confined in the device by two normal-conductor/graphene
junctions. It leads to an additional resonant condition controlling
the transport picture beside the transmission via the bound states
in the barrier. Indeed, the existence of such confined states is
demonstrated clearly from the behavior of LDOS shown in Fig. 6(a).
In this figure, to cancel the effects of bound states in the
barrier, the gate voltage is not applied to the device. The energy
spacing \(E_S\)  is estimated to be about \(25.5\)  meV for \(L_D = 51\)  nm
and \(12.6\)  meV for 102 nm. It means that \(E_S\)  seems to be
inversely proportional to the device length, i. e., as illustrated
in Fig. 6(c). This implies an unusual quantization of charges in the
graphene-based structures, which is essentially different from the
case of normal semicondutors wherein \(E_S \propto 1/L_D^2\)  as
previously discussed in Refs. [1]}, [2]}. Due to such
confinement, the transport quantities, such as the conductance and
the spin current (not shown), have an oscillatory behavior also with
respect to the Fermi energy in the considered region (see in Fig.
6(b)). Therefore, when a gate voltage is applied, there is a
coexistence of bound states in the barrier and confined states in
the device. They together respond for the resonant transport
conditions of the structure.
<FIGURE><FIGURE>